Extension of techniques for differential regularisation and application to non trivial field theories

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Quantum field theory is the basis of modern theoretical physics. The so called standard model which describes very successfully almost all elementary particle physics is a particular quantum field theory. Despite its long history quantum field theories still have significant mathematical problems. Calculations introduce divergences and while these can be circumvented by the ideas of renormalisation the techniques involved are not always satisfactory or mathematically natural.

The technique of differential regularisations has been developed in recent years and provides an approach which circumvents some of these difficulties. As yet it is not fully developed and the project will extend its range of applications and mathematical basis further.

The project aims to: apply the methods differential regularisation to non-trivial quantum field theories, in particular four dimensional gauge field theories and two dimensional non linear sigma models. This will require the application of Ward identities and an analysis of the subtleties of their application in this context; supply formal proofs of the applications of these methods to all orders in the perturbative expansions; and consider applications of the ideas of differential regularisation to supersymmetric field theories and also field theories on curved space backgrounds.

These activities will be undertaken by the participants seperately and jointly when they are visiting each others institutes. The project aims to write joint scientific papers during this period.